Científica
ISSN: 1665-0654
revista@maya.esimez.ipn.mx
Instituto Politécnico Nacional
México
Sauceda Meza, Israel; Hernández Gómez, Luis Héctor; Urriolagoitia Sosa, Guillermo; Beltrán
Fernández, Juan Alfonso; Merchán Cruz, Emmanuel Alejandro; Sandoval Pineda, Juan Manuel;
Velásquez Sánchez, Alejandro Tonatiu
Thermal Fatigue Analysis of an Emergency Core Cooling System Nozzle of a BWR Reactor, by the
Finite Element Metod
Científica, vol. 11, núm. 3, julio-septiembre, 2007, pp. 113-119
Instituto Politécnico Nacional
Distrito Federal, México
Disponible en: http://www.redalyc.org/articulo.oa?id=61411303
Cómo citar el artículo
Número completo
Más información del artículo
Página de la revista en redalyc.org
Sistema de Información Científica
Red de Revistas Científicas de América Latina, el Caribe, España y Portugal
Proyecto académico sin fines de lucro, desarrollado bajo la iniciativa de acceso abierto
Científica Vol. 11 Núm. 3 pp.113-119
© 2007 ESIME-IPN. ISSN 1665-0654. Impreso en México
Thermal Fatigue Analysis of an Emergency
Core Cooling System Nozzle of a BWR
Reactor, by the Finite Element Metod
Israel Sauceda-Meza1
Luis Héctor Hernández-Gómez2
Guillermo Urriolagoitia-Sosa3
Juan Alfonso Beltrán-Fernández2
Emmanuel Alejandro Merchán-Cruz3
Juan Manuel Sandoval-Pineda3
Alejandro Tonatiu Velásquez-Sánchez2
Autonomous University of Baja California Engineering
Faculty. Unidad Universitaria, Blvd. Benito Juárez s/n,
21900, Mexicali, B.C.
2
Superior School of Mechanical and Electrical Engineering,
National Polytechnic Institute. Sección de Estudios de Posgrado
e Investigación; Edificio Núm. 5, Tercer Piso, UPALM, Col.
Lindavista, Delegación Gustavo A. Madero, 07738 , México, DF.
3
Superior School of Mechanical and Electrical Engineering,
National Polytechnic Institute. Unidad Profesional,
Azcapotzalco, Av. de las Granjas No. 682, Col. Sta. Catarina
Azcapotzalco, 02550, México, DF.
MÉXICO.
1
e-mail: israel@uabc.mx
Recibido el 20 de junio de 2006; aceptado el 10 de enero de 2007.
1. Abstract
The evaluation of the fatigue cumulative usage factor for the
High Pressure Core Spray (HPCS) nozzle of a Boiling Water
Reactor (BWR) reactor is developed in this paper. This fatigue
phenomenon is originated mainly due to the sudden injection
of cold water inside the reactor vessel through the before
mentioned nozzle. In this case, there is a thermal shock which
produces high stresses. Therefore, a numerical methodology is
applied, based on the requirements of ASME Code. Firstly the
thermal and transient stress fields are calculated with the Finite
Element Method and secondly the total cumulative usage factor of the HPCS nozzle is evaluated following Miner's criterion.
Key words: thermal stress, fatigue analysis, Miner's criteri
transient thermal-stress analysis, fatigue usage factor.
2. Resumen (Análisis de fatiga térmica en una boquilla d
enfriamiento de un reactor BWR, por el método de
elemento finito)
El objetivo del presente trabajo es desarrollar una metodología
para la evaluación de daño acumulado en boquillas de
inyección de agua de emergencia en recipientes a presión
mediante el elemento finito de acuerdo a lo establecido en e
código ASME. Éstas son utilizadas en sistemas de protección
en reactores de agua en ebullición (BWR), siendo el principa
objetivo bajar la temperatura del núcleo cuando éste aumenta
arriba del rango de operación permisible por medio de una
inyección de agua tratada. Sin embargo, debido a la diferencia
de temperaturas entre la pared del reactor y la boquilla, existe
un choque térmico, éstos generan esfuerzos térmicos altos
que varían cíclicamente, lo cual corresponde al caso de fatiga
de bajo número de ciclos. En consecuencia, esto genera un
daño acumulado que de no controlarse puede conducir a
falla. Esto es evaluado con la regla Miner.
Palabras clave: estrés térmico, análisis de fatiga, regla de Mine
factor de fatigas por uso.
3. Introducción
One of the main problems that the world is facing is the lac
of clean energy for satisfying energy needs all around th
world avoiding enhanced greenhouse effects and globa
warming. Furthermore, the nuclear programs are a good optio
to deal with this problem, they would be reactivated. So
while nuclear option is reactivated the users are taking action
like "License Renewal" and "Power Update" [1, 2 and 3
Therefore, there are two important issues to study i
components important to safety of a Nuclear Power Plant, fo
dealing with the mentioned issues (1) the continuous an
precise monitoring of the cumulative damage in critica
components or locations and, (2) the knowledge about th
shape and geometry of defects and flaws, materia
deterioration, etc (ageing). In both cases, the evaluation o
Científica
consumed life and remaining life is required. So, fatigue
analysis is an important tool for developing them.
Mexico has a Nuclear Power Plant named Laguna Verde (LVNPP)
with two units with Boiling Water Reactors (BWR-5). In this
paper, as an example, the consumed life of the HPCS nozzle (its
internal diameter is 9.67 in) of a BWR generic is analyzed.
Accordingly, a methodology for thermal stress fatigue analysis
is proposed. It is used in conjunction with the Finite Element
Method (FEM) and the ASME Code Section III. For this purpose,
the Palmer-Miner's criterion of cumulative fatigue damage [4] is
used. Although, this criterion is for Linear-Elastic materials and
several simplified considerations are taken into account, the
results obtained are considered acceptable. In the open literature,
there are many cases where its validity is demonstrated as for
example [5]. It is important to mention that the Mexican
regulatory guidance indicates that LVNPP must use the ASME
Code, due to the fact that the reactor proceeds from the United
States of America. For this purpose, an accurate evaluation of
the transient stress field is required. In this paper, the thermal
fatigue analysis of the first twelve water injections is reported,
besides the flexibility introduced by the adjacent pipe is taken
into account in the calculations. The transient pressure is not
considered because a nozzle is considered as thick shell so its
effect is negligible. It is important to mention that thin shells are
susceptible to pressure transients, while they are not affected by
temperature transients.
4. Description of the problem
The HPCS system is part of the Emergency Core Cooling
System (ECCS) and its main purpose is to provide water inside
the Boiling Water Reactor when there is a piping break in
such a way that the heat generated remains under control,
avoiding fuel damage. It has to be kept in mind that the
reactor design conditions establish that the wall of the nozzle is at 528 °F (548.5 °K) like the vessel, at normal conditions,
and when the HPCS system is demanded, water from the
suppression pool or from a condensate tank is injected at 40 °F
(277.4 °K). It is considered, from a theoretical point of view,
that this transient occurs suddenly. In order to avoid a thermal
shock, the nozzle is provided with a jacket or thermal sleeve.
However, the joint of the nozzle and the jacket is under high
stress low cycle fatigue, due to this location is not protected
by the thermal sleeve, besides it has a change of geometry
which produces a high stress concentration.
Nozzles are one of the most important components of the Reactor
Pressure Vessel in a Nuclear Power Plant because they are very
sensitive to thermal fatigue. In this paper, twelve injection cycles
have been considered and these cycles could have been developed
at either lower or higher conditions than those foresight at the
design. Furthermore and for the reasons already mentioned at th
beginning of this paper, it is important to know accurately th
accumulated damage. Due to the fact that stress amplitudes fo
thermal shock are high then the nozzle will sustain adequatel
only a reduced number of cycles. Clearly, this is a problem i
which a transient temperature field is coupled with a stress field i
a complicated geometry. In order to evaluate the phenomeno
FEM was used. For this purpose, the computing infrastructur
available was a Pentium PC with 8 Mbytes in RAM and 51
Mbytes of capacity in its hard disk. ANSYS Code was used for a
the calculations and when the stresses are obtained, the ASM
Code [6] is applied in order to obtain the Cumulative Usage Fac
tor, which must be less than 1.0 in accordance with Miner's ru
and no crack is considered at the nozzle.
5. Methodology
Considering, the computational resources mentioned abov
as well as the nozzle geometry, an axisymmetric model wa
developed. Accordingly, the analysis was divided in thre
main steps.
1. THERMAL-TRANSIENT HEAT TRANSFER ANALYSIS, i
which the following parameters are considered: the temperatur
of the injected water, the operating temperature of the reacto
which remains constant, and the temperature of the surroundin
atmosphere of the nozzle, as well as the forced convectio
heat transfer on the external boundaries of the nozzle.
2. A STRESS ANALYSIS, which evaluates the stresses cause
by the transient temperature gradient during each time step
3. A THERMAL FATIGUE ANALYSIS which is develope
applying ASME Code III requirements in conjunction wit
Miner´s criterion for the evaluation of the cumulative usag
factor.
6. Analysis of the problem
In first instance, a stationary analysis was done, its purpos
was to simulate the operating conditions before the wate
injection. Following this, the transient analysis was performed
Thus, after each step, in which the transient thermal field wa
calculated, the stress evaluation was carried on. Besides, th
arrangement of nozzle with its piping system establishes tw
analysis conditions. In the first case, only the nozzle wa
considered, in the second case, it was assumed that th
adjacent piping, which has an "L" shape, gives an extr
flexibility. These reduced the severity of the transient stres
field. Accordingly, the geometry between the end nozzle an
the first support was considered in the calculations. Therefor
an equivalent straight pipe was calculated, in such way th
Científica
Fig. 1. Mesh used in the nozzle analysis.
both geometries, the proposed and the "L" shape, have an
equivalent stiffness and, afterwards, this was considered in
the axisymetric finite element model.
In both cases, the element selected for the FEM analysis was
PLANE75 axisymetric, in order to take advantage of the computing
equipment capacity. It is a linear rectangular axisymetric element
which can be used in the thermal analysis coupled with the stress
analysis. It has four nodes and each one has three degrees of
freedom [7]. The material of the reactor pressure vessel wall is SA
503 ASTM (low alloy carbon steel) and the material of the nozzle
and thermal sleeve is SB 166 and SA 336.
Fig. 2. Boundary conditions for the thermal and
stress analysis of the case 1.
Figure 2 shows schematically the boundary conditions fo
the thermal and stress analysis. Firstly, the internal wall reac
tor and the sleeve is at 518 °F (543 °K), the wall that direc
the water to the reactor is subjected to a forced convection o
0.347 BTU/h-inch2 °F at 77°F (298 °K), and the external no
zzle surface is subjected to a forced convection of 0.347 BTU
h-inch2 °F at 150 °F (338.5 °K). For the stress analysis, thirty
six nodes at the end that is next to the piping system wer
restricted to move in the "Y" direction. Besides, in the nozzle
end, which is joined to the reactor, 16 nodes were restricte
to move in the radial direction of the nozzle.
6.1. Analysis of the HPCS nozzle
6.2. Analysis of the HPCS nozzle and the equivalen
straight length
The mesh used for the nozzle analysis has 2 575 elements, in
which 1 225 of them were located on the critical zone, which
is the zone where the thermal sleeve and the nozzle are joined
(Figure 1). Note that the elements of the sleeve and above the
shoulder nozzle are smaller. For this reason, the grid
mentioned above is shadowed in this area.
The mesh used in case 2 has 3 800 elements, and is similar t
the one considered in case 1. In this case, the mesh in th
critical zone has 1 225 elements. Figure 3 shows schematicall
the boundary conditions. In the case of the thermal analysi
the same boundary conditions were applied as in the fir
Científica
Tabla 1. Temperatures reported in the twelve
injection cycles (oF).
Injection
cycle
1
2
3
4
5
6
7
8
9
10
11
12
Fig. 3. Boundary conditions for the thermal and
stress analysis of the case 2.
Temperature of reactor
and nozzle
524 (546.3 oK).
445 (502.4 oK).
524 (546.3 oK).
520 (544.1 oK).
523 (545.7 oK).
521 (544.6 oK).
516 (541.8 oK).
526 (547.4 oK).
526 (547.4 oK).
526 (547.4 oK).
527 (548.0 oK).
527 (548.0 oK).
Temperature of
injected water
60.7 (288.9 oK).
77.1 (298.0 oK).
80.2 (299.7 oK).
80.1 (299.7 oK).
78.1 (298.6 oK).
78.2 (298.6 oK).
77.1 (298.0 oK).
77.1 (298.0 oK).
78.2 (298.6 oK).
79.1 (299.1 oK).
60.3 (288.7 oK).
98.4 (309.8 oK).
The stress-time curve of the first injection is shown in graph
1. Initially, the curve is in an steady state, in which th
average stress 686.6 kpsi is under design levels. Afterward
three seconds after the injection, a maximum stress of 256 67
kpsi is developed. From this point, stress tends to be reduce
until steady state is reached again. In all the cases studied
this peak stress was considered for fatigue calculations. I
order to get some knowledge, in a first approach, a fatigu
analysis was performed considering twelve average cycle
with the design conditions. For the first case, the nozzle ha
case. The external wall of the nozzle and the equivalent
straight pipe was subjected to a forced convection of 0.347
BTU/h-inch2 °F at 150 °F (338.5 °K). The internal wall and
jacket reactor temperatures are 518 °F (543 °K) and there is a
forced convection at 0.347 BTU/h-inch2 °F at 77 °F (298 °K)
in the internal wall of the nozzle and the pipe.
Regarding the boundary conditions for the stress analysis,
36 nodes at the end of the equivalent pipe were restricted to
move on the "Y" direction, while 16 nodes at the nozzle's end
that is next to the reactor wall are restricted to move in the
nozzle radial direction.
7. Analysis of the results
The temperatures of the reactor and injected water, which
were reported during each injection cycle, are shown in
table 1. The initial analysis of the transient thermal field,
showed that after 198 seconds, the temperature field tends
to stabilize. However, the stress variation during the cycle
was studied.
Graphic 1. Stress-Time curve.
Científica
Fig. 4. Temperature gradients.
Fig. 5. Thermal stresses.
a temperature field which is in agreement with the boundary
conditions and its gradient is not a severe one, except in the
"A zone" in which, the nozzle and the sleeve are joined
(Figure 4). This implies the development of peak thermal
stresses.
results confirm that the pipe adds flexibility to the nozzl
reducing the peak stresses, with this information, the avera
ge cumulative usage fatigue damage was evaluated. In a
the cases it was used, the design curve of fatigue fo
austenitic steels, nickel-chromium-iron alloy and nicke
copper-alloy of ASME Code Section III Division I [6]. Tab
2 stablishes a comparison among the results obtained fo
the different cases.
The analysis of the maximum principal stress field (Figure 5)
confirms that the stress field is almost uniform on the whole
nozzle body, except on the identified critical zone. In which
the highest peak stress is 256.67 kpsi (1 770 MPa).
The analysis of the temperature distribution of case 2, shows
similar conclusions as those obtained for case 1 (Figure 6),
the main difference is that the maximum peak stress is lower
160.38 kpsi (1 106 MPa) (Figure 7), although it is developed
in the same zone point. In order to explain this result, it
must be considered the fact that the temperature distribution
in the equivalent pipe, reduces the severity of the
temperature gradient in the critical zone. Moreover, these
In the case of the design methodology, it seems that
Discontinuity Stress Analysis was performed, and pea
stresses were developed in the same location observed in th
paper. However, the stresses are lower in this last case due t
the fact that a Discontinuity Analysis is conservative becaus
it applies the deformation compatibility criterion among thi
or thick cylinders, not considering the exact geometry i
transitions or in rounded locations. This explains th
difference between the old methodology and modern FEM
results.
Científica
Fig. 6. Temperature gradients of the case 2.
Fig. 7. Thermal stresses of the case 2.
In a second approach, the cumulative damage was evaluated
injection by injection. In other words, the transient thermal
stresses were calculated with the information reported by the
user (it is shown in table 1). This calculation is a more exact
one than that using average values. The analysis of table 1
shows that, the cycle and design conditions are very similar.
However, the cycle 2 and 12 are not severe. On the other side,
cycles 1 and 11 are critical.
sleeve-piping" component subjected to a coupled Hea
Transfer-Stress phenomenon. It is very useful for studyin
ageing or life extension cases for nuclear power plants. I
this paper, it was calculated the cumulative usage fatigu
factor for a ECCS nozzle of a BWR reactor, considering
Considering the above mentioned and the methodology
proposed in section 3, the cumulative damage was evaluated,
the results shown in both cases are similar. However in case
2, the temperature field and the flexibility introduced by the
pipe arrangement reduced the severity of the peak stresses.
Consequently the accumulated damage is lower.
8. Conclusions
The Finite Element Method permits to develop a precise
analysis of complicated geometries, like a "nozzle-thermal
Tabla 2. Cumulative Usage Factor results.
Methods used
Cummulative usage factor
Using design methodology
11.078 %
Average result by ANSYS
(case 1).
7.059 %
Injection by injection analysis
by ANSYS (case 1).
6.635 %
Average result by ANSYS
(case 2).
4%
Injection by injection analysis
by ANSYS (case 2).
3.759 %
Científica
cycle by cycle damage and the flexibility of the adjacent
piping. Results show that FEM provides lower values than
those obtained with the old design methodology.
The geometry in the critical area, the zone where the thermal
sleeve and the nozzle are joined (Figure 1), plays an important
role on the stress patterrn developed. When a crack is
developed, an interaction with the nozzle boundaries will
take place and the stress intensity factor at the crack tip will
increase, as it was observed in [8]. Besides, local material
imperfections and strain rate will affect the direction and
stability of the crack propagation [9,10].
Acknowledgements
The grants awarded by CONACYT (3761P-A9608), DEPI
(964913) and COFAA are kindly acknowledged.
9. References
[1] L. H. Hernández-Gómez and P. Ruiz-López, «Basis and
criteria for an aging assessment program of mayor
components in Mexican Nuclear Installations».
Proceedings of an International Symposium on
Materials Ageing and Component Life Extension.
Milan Italy Vol II, 1411-1419 (1995).
[2] J. L. Medina-Velarde, L. H. Hernández-Gómez, G.
Urriolagoitia-Sosa, G. Villa y Rabasa, H. H. VázquezMendoza and G. Urriolagoitia-Calderón, «Análisis
tridimensional de transferencia de calor en componentes mecánicos de reactores nucleares por el método del
elemento finito», Científica, Año 1, Núm 3, Mayo-Ju
nio, pp 33-39 (1997).
[3] G. Urriolagoitia-Calderón, L. H. Hernández- Gómez, G
Villa y Rabasa, G. Urriolagoitia-Calderón, J. L. Medina
Velarde, G. Urriolagoitia-Sosa, H. H. Vazquez-Mendoz
and C. León-Vega, «Solución conceptual del compo
tamiento de una probeta agrietada sometida a cargas d
fatiga para determinar su vida remanente», Científica
Año 1, Núm 5, Septiembre-Octubre, pp 39-42 (1997)
[4] M. A. Miner and S. Monica,» Cumulative Damage in Fa
tigue», J. Appl. Mech, Vol 12, 3 (1945).
[5] M. Jiang, Damage, «Evaluation model for strain fatigu
of ductile metals». Engineering Fracture Mechanic
Vol 52, No 6, pp. 971 - 975 (1995).
[6] ASME Boiler and Pressure Vessel Code, Section III, 198
Edition (and Section VIII, Division 2).
[7] ANSYS Manual User's, Volume 1: Elements. Swanso
Analysis System (1992).
[8] R. G. Rodríguez-Cañizo, L. H. Hernández- Gómez and G
Urriolagoitia-Calderón, «Análisis de la interacción d
grietas en placas». Revista Mexicana de Física, Vo
51 Suplemento 1, 5-10 (2005).
[9] G. Urriolagoitia-Calderón and L. H. Hernández-Góme
«Experimental analysis of crack propagation stabilit
in single edge notch specimens», Theoretical an
Applied Fracture Mechanics, Vol. 28, 57-68 (1997).
[10] L. H. Hernández-Gómez, I. Sauceda-Meza, G
Urriolagoitia-Calderón, A. S. Balankin and O. Susarrey
«Evaluation of crack initiation angle under mixed mod
loading at diverse strain rates», Theoretical and Applie
Fracture Mechanics. 42, 53-61 (2004).
R EDALYC
Red de revistas científicas de América Latina
y el Caribe, España y Portugal (UAEM)
www.redalyc.org